3/8/2019

3/08/2019

Met with Professor Kruse that Friday morning in his office. We discussed my future (analysis, stochastics, probability theory) and how we could approach a mathematics project that could possibly correlate with Biology. We discussed a few ideas:

a) Using linear algebra to model a "least squares" model to show a algebraic relationship to regressions used in statistical analysis. The idea would have been to mathematically define this relationship, and use MATLAB to model it. Although intriguing, I did not find it beneficial to my skill development, or as a stand-out maths/biology project.

b) Using partial differential equations to develop an accurate weather model that would take time and space into consideration. Although my favorite idea, it seemed a bit too complex to model without a research professor who specialized specifically in PDEs.

c) using ordinary differential equations to develop a mathematical model that would show the birth, spread, and death of a disease using the SRI model. This could work out pretty well, because it correlates with biology and will allow me to utilize knowledge I can gain from the Biology department at GCC, and I will be able to have an applied mathematics project under my belt.

The next foreseeable steps are to study the SRI model and gather data for some virus or infection, preferably within the last few years and in the Phoenix area.

Comments

Post a Comment

Popular posts from this blog

4/9/2019

Image
I met with Prof Kruse this past Friday, and we talked about how the SIR model works and the derivation of the differential equations. The following are questions I have answered from Duke University's SIR epidemic model example guide. Our next steps are working more on practicing the model, and fitting a mathematically defined function to fit a real data set.   Under the assumptions we have made, how do you think  s(t)  should vary with time? How should  r(t)  vary with time? How should  i(t)  vary with time? Before the spread of an infection, the amount susceptible to the infection within a population will naturally be close enough to the population, that the difference is negligible. So we can use the constant N to equal our population. If we are modelling as a fraction, we may divide throughout the equation by our population constant, N. The interaction between the infected and susceptible population will cause a loss ...
Read more

4/14/2019

Image
Topics Covered: Euler's method for approximation Curve fitting Relating Model Parameters to Data Defining the "contact" coefficients Tools/Resources used: MATLAB Duke University's SIR guide Keeling and Rohani's Modeling Infectious Diseases In Humans and Animal This past week, I was able to finally apply some of the resources and tools I have acquired to make progress on intuitively understanding the SIR model for infectious diseases. After understanding how the model is broken down mathematically, I needed to understand how the system of ODEs (ordinary differential equations) interacted with each other. There are many ways to solve systems of ODEs, i.e. laplace, eigenvalues, matrix manipulation, etc. For the purpose of approximating the solutions to these differential equations at given times, we will be using Euler's method. In fact, Euler's method is simple and direct. It involves relating the slope to the step size. Unfortunately, it can b...
Read more

3/19/2019

Image
Over the past few days, I have kept in contact with Prof. Kruse and Dr. Tuohy to determine the best path to prep myself to tackle the problem of mathematically modelling an infection. Additionally, to better research infection models, I have ordered  Keeling and Rohani's Modeling Infectious Diseases In Humans and Animals . I think it would provide modern insight on biology jargon and infection modeling. Prof. Kruse recommended that I utilize Duke University's SIR Model examples with downloadable MATLAB examples. This is an excellent resource thus far, and has provided me with modeling techniques on MATLAB, as well as insight on how to read the SIR model. The utility can be found here: https://services.math.duke.edu/education/ccp/materials/diffcalc/sir/contents.html I have made some progress, and am still developing a full understanding of the SIR model. The Duke SIR utility comes with questions that I will look to answer in the following blog posts. Also today, I was ha...
Read more